4 A particle \(A\), moving along a straight horizontal track with constant speed \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), passes a fixed point \(O\). Four seconds later, another particle \(B\) passes \(O\), moving along a parallel track in the same direction as \(A\). Particle \(B\) has speed \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) when it passes \(O\) and has a constant deceleration of \(2 \mathrm {~m} \mathrm {~s} ^ { - 2 } . B\) comes to rest when it returns to \(O\).

1. Find expressions, in terms of \(t\), for the displacement from \(O\) of each particle \(t\) seconds after \(B\) passes \(O\).
2. Find the values of \(t\) when the particles are the same distance from \(O\).
3. On the given axes, sketch the displacement-time graphs for both particles, for values of \(t\) from 0 to 20 .
   \includegraphics[max width=\textwidth, alt={}, center]{4ee2568e-5902-442f-9af1-3663fa1d59c7-07_805_1259_1672_484}
   \includegraphics[max width=\textwidth, alt={}, center]{4ee2568e-5902-442f-9af1-3663fa1d59c7-08_467_583_255_781} A block of mass 12 kg is placed on a plane which is inclined at an angle of \(24 ^ { \circ }\) to the horizontal. A light string, making an angle of \(36 ^ { \circ }\) above a line of greatest slope, is attached to the block. The tension in the string is 65 N (see diagram). The coefficient of friction between the block and plane is \(\mu\). The block is in limiting equilibrium and is on the point of sliding up the plane. Find \(\mu\).